The aim of this paper is to study the dynamics of the US real effective exchange rate by capturing non-linearity and long-memory features. In this context, we use the family of fractionally integrated STAR (FISTAR) models proposed by van Dijk et al. (van Dijk, D., Franses, P.H., and Paap, R., 2002. A non-linear longmemory model with an application to US unemployment. Journal of Econometrics 110, 135-165.) in the case when the transition function is an exponential function and we develop an estimation procedure. Indeed, these models can take into account processes characterized by several distinct dynamic regimes and persistence phenomena.

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